Graduation Year

2007

Document Type

Thesis

Degree

M.A.

Degree Granting Department

Mathematics

Major Professor

Wen-Xiu Ma, Ph.D.

Co-Major Professor

Yuncheng You, Ph.D.

Committee Member

Athanassios G. Kartsatos, Ph.D.

Keywords

The tanh method, PDE, KdV, Solitary wave, Wave equation

Abstract

In this thesis, first the tanh method, a method for obtaining exact traveling wave solutions to nonlinear differential equations, is introduced and described. Then the method is applied to two classes of Nonlinear Partial Differential Equations. The first one is a system of two (1 + 1)-dimensional nonlinear Korteweg-de Vries (KdV) type equations. The second one is a (3 + 1)-dimensional nonlinear wave equation. At the end, a few graphic representations of the obtained solitary wave solutions are provided, in correspondence to different values of the parameters used in the equations.

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